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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate : $\int \large\frac{6}{7} . \frac {e^{\sqrt x}. \cos (e^{\sqrt x})}{\sqrt x }$$dx$

$(a)\;\frac{12}{7}\cos (e^{\sqrt x})+c \qquad(b)\;\frac{12}{7}\sin (e^{\sqrt x})+c \qquad(c)\;\frac{12}{7}\sin (e^{x})+c \qquad (d)\;\frac{12}{7}\cos (e^{\sqrt x})+c$

1 Answer

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$e^{\sqrt x}=t$
Differentiate with respect to x
$e^{\sqrt {x}} \times \large\frac{1}{2 \sqrt x }$$dx=dt$
=> $\large\frac{e^{\sqrt x}}{\sqrt x}$$ dx=2 dt$
=> $\large\frac{6}{7} $$ \int 2. \cos t. dt$
=> $\large\frac{12}{7}$$ \sin t +c$
=> $\large\frac{12}{7}$$ \sin (e^{\sqrt x}) +c$
Hence b is the correct answer.
answered Dec 24, 2013 by meena.p